Finding the Change of Coordinate Matrix for Standard and Custom Bases

[Punkyc7]

Find the change of coordinate matrix from$$\gamma$$ coordinates to $$\beta$$ coordinate where $$\beta$$ is the standard basis for P2(R) and
$$\gamma$$={ 1+t^2, t-t^2, 1-2t +t^2}

Since i can't figure out how to type matrices i will explain what I did. I made a 3 by 3 matrix and put the $$\beta$$ basis on the top of the matrix and the $$\gamma$$ basis on the row side. The I got the matrix
101
01-1
1-21

Im wondering if this is right or if I put the bases on the wrong part of the matrix because I can never remember where they go.

 

[Dick]

If your matrix is supposed to act on the vector {1,t,t^2} and produce the vector {1+t^2, t-t^2, 1-2t +t^2} then I think you have it right.